An image can be formed by dots located within pixels that are arranged in vertical columns and horizontal rows. When an analog wave is displayed with its time axis parallel to the rows and without any smoothing, it will appear as a series of dots, one in each column at a height corresponding to the amplitude of the wave. If the amplitude changes rapidly, gaps appear between consecutive dots. The gaps can be closed by adding auxiliary dots, as indicated in FIG. 1A wherein M designates dots formed at the intersection of a wave with a column; but, as can be seen, steps are formed that give the representation of the wave a jagged appearance. The steps can be essentially eliminated by forming generally diamond-shaped patterns along each column having ends that dovetail so as to fit together and form a smooth line, as described in U.S. Pat. No. 4,212,009, issued on July 8, 1980, to George L. Adleman et al. One particular algorithm for forming the patterns is illustrated by the chart below wherein T.sub.n is the amplitude of the analog wave at a given column of pixels and T.sub.n-1 , T.sub.n-2, T.sub.n-3 and T.sub.n-4 are its amplitudes at respectively previous columns. Three "3"s indicate a maximum size dot having a diameter of two columns; two "2"s indicate a dot having two-thirds the maximum size; and a "1" indicates a dot having one-third the maximum size.
______________________________________ T.sub.n-4 T.sub.n-3 T.sub.n-2 T.sub.n-1 T.sub.n . . . . . . . . . . . . . . n . . . . 1 . . . . 22 . . . n . . . 333 . . . . 333 . . . 1 333 . . . 1 333 . . . 22 333 . . . 22 333 . . n . . . 333 . . . 22 . . . 333 22 . . . . . . 333 . . . 22 . . 1 333 1 . . 1 333 1 . . 1 . . . 333 . . . 1 . . 22 333 . . . 22 333 . . . 22 . . . 333 . . n 333 22 . . 1 333 1 . . 22 333 . . n 333 22 . . ______________________________________
FIG. 1B illustrates two patterns D.sub.1 and D.sub.2 that result from using the algorithm defined by the chart when smoothing a straight line.
Vertical smoothing, however, does not reduce the discontinuities that are formed between horizontal line segments that are one row apart.